Continuum limit of $p$-biharmonic equations on graphs

arXiv:2404.19689v1 Announce Type: cross
Abstract: This paper studies the $p$-biharmonic equation on graphs, which arises in point cloud processing and can be interpreted as a natural extension of the graph $p$-Laplacian from the perspective of hypergraph. The asymptotic behavior of the solution is investigated when the random geometric graph is considered and the number of data points goes to infinity. We show that the continuum limit is an appropriately weighted $p$-biharmonic equation with homogeneous Neumann boundary conditions. The result relies …

abstract arxiv behavior cloud cs.lg cs.na equation extension graph graphs hypergraph interpreted math.ap math.na natural paper perspective processing random solution studies the graph type